As we begin to reach the limits of classical computing, quantum computing has emerged as a technology that has captured the imagination of the scientific world. While for many years, the ability to ...execute quantum algorithms was only a theoretical possibility, recent advances in hardware mean that quantum computing devices now exist that can carry out quantum computation on a limited scale. Thus, it is now a real possibility, and of central importance at this time, to assess the potential impact of quantum computers on real problems of interest. One of the earliest and most compelling applications for quantum computers is Feynman’s idea of simulating quantum systems with many degrees of freedom. Such systems are found across chemistry, physics, and materials science. The particular way in which quantum computing extends classical computing means that one cannot expect arbitrary simulations to be sped up by a quantum computer, thus one must carefully identify areas where quantum advantage may be achieved. In this review, we briefly describe central problems in chemistry and materials science, in areas of electronic structure, quantum statistical mechanics, and quantum dynamics that are of potential interest for solution on a quantum computer. We then take a detailed snapshot of current progress in quantum algorithms for ground-state, dynamics, and thermal-state simulation and analyze their strengths and weaknesses for future developments.
The accurate computation of Hamiltonian ground, excited and thermal states on quantum computers stands to impact many problems in the physical and computer sciences, from quantum simulation to ...machine learning. Given the challenges posed in constructing large-scale quantum computers, these tasks should be carried out in a resource-efficient way. In this regard, existing techniques based on phase estimation or variational algorithms display potential disadvantages; phase estimation requires deep circuits with ancillae, that are hard to execute reliably without error correction, while variational algorithms, while flexible with respect to circuit depth, entail additional high-dimensional classical optimization. Here, we introduce the quantum imaginary time evolution and quantum Lanczos algorithms, which are analogues of classical algorithms for finding ground and excited states. Compared with their classical counterparts, they require exponentially less space and time per iteration, and can be implemented without deep circuits and ancillae, or high-dimensional optimization. We furthermore discuss quantum imaginary time evolution as a subroutine to generate Gibbs averages through an analogue of minimally entangled typical thermal states. Finally, we demonstrate the potential of these algorithms via an implementation using exact classical emulation as well as through prototype circuits on the Rigetti quantum virtual machine and Aspen-1 quantum processing unit.The quantum imaginary time evolution and Lanczos algorithms offer a resource-efficient way to compute ground or excited states of target Hamiltonians on quantum computers. This offers promise for quantum simulation on near-term noisy devices.
We describe an algorithm to reduce the cost of auxiliary-field quantum Monte Carlo (AFQMC) calculations for the electronic structure problem. The technique uses a nested low-rank factorization of the ...electron repulsion integral (ERI). While the cost of conventional AFQMC calculations in Gaussian bases scales as O ( N 4 ) , where N is the size of the basis, we show that ground-state energies can be computed through tensor decomposition with reduced memory requirements and subquartic scaling. The algorithm is applied to hydrogen chains and square grids, water clusters, and hexagonal BN. In all cases, we observe significant memory savings and, for larger systems, reduced, subquartic simulation time.
We demonstrate a method that merges the quantum filter diagonalization (QFD) approach for hybrid quantum-classical solution of the time-independent electronic Schrödinger equation with a low-rank ...double factorization (DF) approach for the representation of the electronic Hamiltonian. In particular, we explore the use of a novel sparse “compressed” double factorization (C-DF) truncation of the Hamiltonian within the time-propagation elements of QFD, while retaining a similarly compressed but numerically converged double-factorized representation of the Hamiltonian for the operator expectation values needed in the QFD quantum matrix elements. The new C-DF method is found to provide substantial additional compression at any given accuracy metric over the traditional “explicit” double factorization approach. Together with significant circuit reduction optimizations and number-preserving postselection and echo-sequencing error mitigation strategies, the method is found to provide accurate predictions for low-lying eigenspectra in a number of representative molecular systems, while requiring reasonably short circuit depths and modest measurement costs. The method is demonstrated by experiments on noise-free simulators, simulations including models of decoherence and shot-noise, and real quantum hardware.
Quantum simulation on emerging quantum hardware is a topic of intense interest. While many studies focus on computing ground-state properties or simulating unitary dynamics of closed systems, open ...quantum systems are an interesting target of study owing to their ubiquity and rich physical behavior. However, their nonunitary dynamics are also not natural to simulate on digital quantum devices. Here, we report algorithms for the digital quantum simulation of the dynamics of open quantum systems governed by a Lindblad equation using adaptations of the quantum imaginary–time evolution algorithm. We demonstrate the algorithms on IBM Quantum’s hardware with simulations of the spontaneous emission of a two-level system and the dissipative transverse field Ising model. Our work advances efforts to simulate the dynamics of open quantum systems on quantum hardware.
Quantum computers are promising for simulations of chemical and physical systems, but the limited capabilities of today’s quantum processors permit only small, and often approximate, simulations. ...Here we present a method, classical entanglement forging, that harnesses classical resources to capture quantum correlations and double the size of the system that can be simulated on quantum hardware. Shifting some of the computation to classical postprocessing allows us to represent ten spin orbitals of the water molecule on five qubits of an IBM Quantum processor in the most accurate variational simulation of the H_{2}O ground-state energy using quantum hardware to date. We discuss conditions for applicability of classical entanglement forging and present a roadmap for scaling to larger problems.
Net-zero climate districts are gaining wide attention at the European and international levels. Urban regeneration competitions have been launched recently to stimulate development; nevertheless, the ...literature does not yet provide a shared scope definition (i.e., product system). Using the process-based life cycle assessment method, the authors evaluate the climate profile of a new district in Milan (14 buildings with 36,000 m2 of gross surface area in total) aiming to become the first net-zero social housing project in Italy. The authors show in the results section how climate neutrality is achieved on the part of the real estate operator by varying the scope. The most conservative scenario (including all the emission sources considered in the analysis) indicates that the net-zero climate target is reached only by purchasing voluntary carbon credits. The authors also highlight: (i) a district composed of nearly-zero energy buildings is far from the definition of a net-zero climate emissions district; (ii) a net-zero climate emissions district may not be a positive energy district and vice-versa; and (iii) constraints linked with the lack of space in a densely populated city due to insufficient area to install renewables on site.
Developing scalable quantum algorithms to study finite-temperature physics of quantum many-body systems has attracted considerable interest due to recent advancements in quantum hardware. However, ...such algorithms in their present form require resources that exceed the capabilities of current quantum computers except for a limited range of system sizes and observables. Here, we report calculations of finite-temperature properties, including energy, static and dynamical correlation functions, and excitation spectra of spin systems with up to four sites on five-qubit IBM Quantum devices. These calculations are performed using the quantum imaginary time evolution (QITE) algorithm and made possible by several algorithmic improvements, including a method to exploit symmetries that reduces the quantum resources required by QITE, circuit optimization procedures to reduce circuit depth, and error-mitigation techniques to improve the quality of raw hardware data. Our work demonstrates that the ansatz-independent QITE algorithm is capable of computing diverse finite-temperature observables on near-term quantum devices.
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